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We present a range-separated linear-response time-dependent density-functional theory (TDDFT) which combines a density-functional approximation for the short-range response kernel and a frequency-dependent second-order Bethe-Salpeter…

Gross-Oliveira-Kohn density-functional theory (GOK-DFT) for ensembles is the DFT analog of state-averaged wavefunction-based (SA-WF) methods. In GOK-DFT, the state-averaged (so-called ensemble) exchange-correlation (xc) energy is described…

This chapter provides a basic introduction to excited-state extensions of density functional theory (DFT), including time-dependent (TD-)DFT in both its linear-response and its explicitly time-dependent formulations. As applied to the…

Density estimation is a fundamental task in statistics and machine learning applications. Kernel density estimation is a powerful tool for non-parametric density estimation in low dimensions; however, its performance is poor in higher…

Koopman Mode Decomposition (KMD) is a technique of nonlinear time-series analysis that originates from point spectrum of the Koopman operator defined for an underlying nonlinear dynamical system. We present a numerical algorithm of KMD…

In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory (DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be…

Calibrating for direction-dependent ionospheric distortions in visibility data is one of the main technical challenges that must be overcome to advance low-frequency radio astronomy. In this paper, we propose a novel probabilistic,…

Gaussian process regression is a powerful method for predicting states based on given data. It has been successfully applied for probabilistic predictions of structural systems to quantify, for example, the crack growth in mechanical…

Density functional theory (DFT) and thermal DFT (thDFT) calculations were used to evaluate the energy band structure, bandgap, and the total energy of various graphene quantum dots (GQDs). The DFT calculations were performed using local…

Accurate phase diagram calculation from molecular dynamics requires systematic treatment and convergence of statistical averages. In this work we propose a Gaussian process regression based framework for reconstructing the free energy…

We demonstrate the capabilities of time-dependent density functional theory (TDDFT) for strong-field, short wavelength (soft X-ray) physics, as compared to a formalism based on rate equations. We find that TDDFT provides a very good…

We formulate the Kohn-Sham density functional theory (KS-DFT) as a statistical theory in which the electron density is deter-mined from an average of correlated stochastic densities in a trace formula. The key idea is that it is sufficient…

We reexamine results obtained with the recently proposed density functional theory framework based on forces (force-DFT) [Tschopp et al., Phys. Rev. E 106, 014115 (2022)]. We compare inhomogeneous density profiles for hard sphere fluids to…

Polymer self-consistent field theory techniques are used to derive quantum density functional theory without the use of the theorems of density functional theory. Instead, a free energy is obtained from a partition function that is…

Tracking control for soft robots is challenging due to uncertainties in the system model and environment. Using high feedback gains to overcome this issue results in an increasing stiffness that clearly destroys the inherent safety property…

Density-potential functional theory (DPFT) is an alternative formulation of orbital-free density functional theory that may be suitable for modeling the electronic structure of large systems. To date, DPFT has been applied mainly to quantum…

Density functional theory (DFT) has been actively used and developed recently. DFT is an efficient instrument for describing a wide range of nanoscale phenomena: wetting transition, capillary condensation, adsorption, and others. In this…

The density functional theory (DFT) is a remarkably successful theory of electronic structure of matter. At the foundation of this theory lies the Kohn-Sham (KS) equation. In this paper, we describe the long-time behaviour of the…

Density fitting is used throughout quantum chemistry to simplify the electron-electron interaction energy (EE). A fundamental property of quantum chemistry, and DFT in particular, is that a variational principle connects the EE to a…

Markov Chain Monte Carlo approach is frequently used within Bayesian framework to sample the target posterior distribution. Its efficiency strongly depends on the proposal used to build the chain. The best jump proposal is the one that…